# What Is the Relationship Between Risk and Return

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Saxo Group

There are good and back aspects to anything in life, and there are tradeoffs between choices. You could choose to rent an apartment. You have a place to live, but you don’t have to worry about maintaining the property. The landlord is responsible for upkeep, repairs, landscaping, etc. At the same time, rent is likely to increase over time and you have no ownership in the property. On the other hand, if you buy a house, the opposite is true. You are responsible to the wellbeing of the property, but will benefit from any increase in the value of the property.

Investments are the Same

The value of investments can go up, which, of course, is good. The value of investments can go down, which, of course, is bad. The ebb and flow of the value of investments is referred to as risk. In this article, we provide some historical numerical examples in order to further explain this concept. We also want to think about how investors are compensated for accepting risk.

Understanding average returns

On average U.S. large-cap stocks have returned or grown by 11.9% per year. On average, if you were to invest \$100 in U.S. large-cap stocks the investment would grow by \$11.90 in a year and the ending value of this investment would be \$111.90 after one year. However, this is just the average return. One year the investment might go up by 30% and in another year, it might go down by 6%. There is some uncertainty surrounding the average return.

What is standard deviation*?

Standard deviation is a statistical measure of how different the returns of an investment can be from the average return on the investment. In the case of U.S. large-cap stocks the standard deviation is 19.8% and it defines a range and probability around the average. The average (11.9%) minus one standard deviation (19.8%) equals -7.9% (11.9% - 19.8%), and the average (11.9%) plus one standard deviation (19.8%) equals 37.1% (11.9% + 19.8%). Translated, this means you would expect the one-year return on U.S. large-cap stocks to be between -7.9% and 37.1% roughly two-thirds of the time, below -7.9% roughly one-sixths of the time and above 37.1% roughly one-sixths of the time. Standard deviation is the most common measurement of the risk of an investment.

More risk – more return

Look at the table of asset class returns and standard deviations.

See mathematical aside* table – Asset Class Returns for U.S. Financial Markets

Notice that, in general, the higher the average return the higher the risk and the higher the risk the higher the average return. U.S. small-cap stock have a higher average annual return than U.S. large-cap stocks, but they also have more risk. The investment journey of U.S. small-cap stocks is more uncertain and with bigger losses and bigger gains along the way.

Compounding

An increase in risk also negatively affects the compounding and growth of your investments. The easiest way to think about this is to understand that if your investment falls by 50% from \$100 to \$50, it will have to grow by 100% to grow from \$50 back to your original investment of \$100. Notice that the higher the standard deviation the larger the difference between the average annual return and the average compound return.

See mathematical aside* table – Average Annual Returns vs. Average Compound Returns

Compensation

Finally, returns are good and risk is bad. Investors typically think about higher returns for riskier assets as compensation for accepting the extra risk.

Mathematical Aside*

 Asset Class Returns for U.S. Financial Markets Average Annual Return Risk (Standard Deviation) Small-Cap Stocks 16.2% 31.6% Large-Cap Stocks 11.9% 19.8% Long-Term Corporate Bonds 6.3% 8.4% Long-Term Government Bonds 5.9% 9.8% Intermediate-Term Government Bonds 5.2% 5.6% 30-Day Treasury Bills 3.4% 3.1% Inflation 3.0% 4.0%
 Average Annual Returns vs. Average Compound Returns Average Annual Return Standard Deviation (Risk) Small-Cap Stocks 16.2% 11.8% Large-Cap Stocks 11.9% 10.0% Long-Term Corporate Bonds 6.3% 5.9% Long-Term Government Bonds 5.9% 5.5% Intermediate-Term Government Bonds 5.2% 5.1% 30-Day Treasury Bills 3.4% 3.3% Inflation 3.0% 2.9%

*We work hard to make these articles as approachable and math-free as possible. At the same time, if a little math makes the article easier to understand, we’ll go ahead and do that too.

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